00:01
So we've been given a population with a mean, mu, population mean, 530, sigma, population standard deviation, 33.
00:10
And we take many samples of size 49.
00:13
And we want to know what the mean of the sample means would be, the standard deviation of the sample means, and the shape.
00:19
So this question relies on the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed compared to the population.
00:32
If n is at least 30, they are approximately normally distributed, regardless of population shape.
00:39
So that's part c, answered, approximately normal.
00:45
The theorem also tells you the mean and standard deviation.
00:50
The mean of the means is the same as the population mean, so 530.
00:56
The standard deviation of the sample means, or standard error, is sigma over root n.
01:03
So that's 33 over root 49.
01:06
33 over 7 is 4 .71 to two decimal places.
01:12
For these two facts, they rely on a piece of knowledge that the mean of x plus y is equal to mean of x plus mean of y...
